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A025457
Number of partitions of n into 4 positive cubes.
10
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1
OFFSET
0,220
COMMENTS
The first term > 1 is a(219) = 2. - Michel Marcus, Apr 23 2019
FORMULA
a(n) = [x^n y^4] Product_{k>=1} 1/(1 - y*x^(k^3)). - Ilya Gutkovskiy, Apr 23 2019
MAPLE
N:= 100;
A:= Array(0..N);
for a from 1 to floor(N^(1/3)) do
for b from a to floor((N-a^3)^(1/3)) do
for c from b to floor((N-a^3-b^3)^(1/3)) do
for d from c to floor((N-a^3-b^3-c^3)^(1/3)) do
n:= a^3 + b^3 + c^3 + d^3;
A[n]:= A[n]+1;
od od od od:
seq(A[n], n=0..N); # Robert Israel, Aug 18 2014
A025457 := proc(n)
local a, x, y, z, ucu ;
a := 0 ;
for x from 1 do
if 4*x^3 > n then
return a;
end if;
for y from x do
if x^3+3*y^3 > n then
break;
end if;
for z from y do
if x^3+y^3+2*z^3 > n then
break;
end if;
ucu := n-x^3-y^3-z^3 ;
if isA000578(ucu) then
a := a+1 ;
end if;
end do:
end do:
end do:
end proc: # R. J. Mathar, Sep 15 2015
MATHEMATICA
r[n_] := Reduce[0 < a <= b <= c <= d && n == a^3+b^3+c^3+d^3, {a, b, c, d}, Integers];
a[n_] := Which[rn = r[n]; rn === False, 0, rn[[0]] === And, 1, rn[[0]] === Or, Length[rn], True, Print["error ", rn]];
Table[a[n], {n, 0, 107}] (* Jean-François Alcover, Feb 26 2019 *)
CROSSREFS
Cf. A003108, A025455, A025456, A025403-A025407, A003327, A025420 (greedy inverse).
Sequence in context: A359150 A354031 A354035 * A350289 A219463 A286688
KEYWORD
nonn
EXTENSIONS
Second offset from Michel Marcus, Apr 23 2019
STATUS
approved